Problem: $tu - 8tv - 6t + 10 = -8u - 4$ Solve for $t$.
Explanation: Combine constant terms on the right. $tu - 8tv - 6t + {10} = -8u - {4}$ $tu - 8tv - 6t = -8u - {14}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $1{t}u - 8{t}v - 6{t} = -8u - 14$ Factor out the $t$ ${t} \cdot \left( u - 8v - 6 \right) = -8u - 14$ Isolate the $t$ $t \cdot \left( {u - 8v - 6} \right) = -8u - 14$ $t = \dfrac{ -8u - 14 }{ {u - 8v - 6} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{8u + 14}{-u + 8v + 6}$